Tag Archives: Limericks

Fibonacci series in nature


Today I will tell you about a concept of mathematics and then apply it to biology, music, history, poetry, literature.
In fact, I will show you the world with this one concept.

Lets take a series of numbers:

1, 1 , 2 , 3, 5, 8, 13, 21, 34, 55, 89…….

Each number is just the sum of previous 2 numbers. So we start with 1 and 1. Add to make 2. Then we add
the 2 to the one before it and get 3. 5 is got by adding 3 and 2. And it goes on and on forever. You can check
that 89 is formed by adding 55 and 34. Of course we can add 89 and 55 to find the next number in the sequence.
So every number is the sum of its immediately 2 previous numbers.

This series is known as the Fibonacci series after a person named Leonardo of Pisa, also known as
Fibonacci, who studied it in detail in 1202 AD. The numbers in this series are called Fibonacci numbers. So 89
is a Fibonacci number but 85 is not.

Fibonacci numbers had always been known to Indian mathematicians. Pingala in 200 BC had used this number
sequence in describing the metrical structure of Sanskrit poetry. All of Sanskrit poetry is based on Fibonacci numbers!

Virgil used the Fibonacci sequence to structure his epic poem Aeneid.

There are studies that state that Beethoven and Mozart used this series of numbers while composing their music.

Now, lets examine the beauty of different kinds of flowers using the Fibonacci number sequence.
A sunflower is beautiful isn’t it? Now lets take a look at its mathematical beauty. If you look into the seeds at the
centre of the flower, you will see them arranged in a tightly packet spiral. The number of spirals is a Fibonacci
number. So you can have 34 spirals inside the sunflower but not 35 or 33. 34 is a Fibonacci number as we have
seen above!

How many petals does a buttercup have : 5 ( it is a Fibonacci number).
How many does a marigold have? 13( Fibonacci number).
How many does an aster have? 21 ( Fibonacci no!).
How many does a daisy have ? 34, 55 or 89 ( ALL FIBONACCI NUMBERS!)

The petals of all flowers follow the Fibonacci number sequence! The number of leaves on a plant in each turn as
you go from bottom to top follow the Fibonacci sequence! Pine cones have a Fibonacci number of spirals and “petals”
at every set of “winding”. Same is true for pineapples!


Leonardo Da Vinci knew about this. He suggested that plants and flowers set themselves up in such a way so as
to preserve moisture. Leonardo Da Vinci used the Fibonacci number sequence in his painting: Mona Lisa and in
the study of the proportions of man, ” The Vetruvian man”.

A golden rectangle is the one whose sides are the ratios of any two consecutive Fibonacci numbers. Divide any
Fibonacci number by its previous and you get about 1.6. So a golden rectangle is one whose sides are of the
ratio 1.6. So a rectangle with the sides 34 and 21 is a golden rectangle because the sides are Fibonacci numbers.
A golden rectangle is most pleasing to the eye. So since time immemorial, artists have employed it in their art and
architects have employed it in their buildings.

Nature is a painter, a musician, a thinker, a philosopher and a great mathematician. Mathematics is Nature’s
attempts to create beauty in numbers. Nature is beautiful; Mathematics is beautiful. There is no other way!

Now let’s learn a very interesting thing about honeybees. I have two parents. You have two parents. All animals
have two parents. But a honeybee is different! It can have one or two parents! A queen bee lays down many
eggs. If an egg is fertilized by a male drone, it hatches to be a female. But if an egg remains unfertilized then
it hatches to be a male drone. So, a male bee only has a mummy! A female bee has a mummy and a daddy!
Females usually end up as worker bees but some( very few) are fed a special kind of jelly which makes them
queens- they fly away to form their own colonies.

Now lets take a male bee. How many parents does it have? 1: the queen female.
How many grand parents does it have : 2 ( the queen female has to have a father and a mother)
How many great grand parents does it have : 3 ( The father will have only a mother but the mother will have two parents)
How many great-great grand parents does it have : 5 ( two for the each of the great grand mothers. One for the great grand father)
How many great great great grand parents: 8 ( you can calculate this….. it is simple)
How many great-4 grand parents: 13
How many great-5 grand parents: 21
How many great-6 grand parents : 34
How many great -7 grand parents : 55
How many great-8 grand parents: 89


This is the Fibonacci series! So the number of ancestors of honey bees at each generation follows the Fibonacci series!
Isn’t this WOW! This is true for the female bee also!

Isn’t the mathematical structure of Nature beautiful?

Now let me tell you about limerick. A Limerick is a 5 line poem with the rhyming sequence: AABBA.
It is always a funny poem and has the following structure: The 1,2 and 5th lines are longer and the 3rd and 4 th
lines are shorter. They are shorter by a metrical foot. The 1,2 and 5 lines should have 9 syllables and the 3rd and 4th
lines have 6 syllables. That is the structure. Here is an example:

This is Dixon Merrit’s famous limerick on pelicans. It has become so popular that it has been quoted several times
in scholarly books of Ornithology. Here it is:

        A wonderful bird is the pelican,
        His bill will hold more than his belican,
        He can take in his beak
        Enough food for a week
        But I’m damned if I see how the helican!

Inspired by this and in reference to our above discussion about Fibonacci numbers and bees, I have written a

The fibonacci number sequence,
is for the bees of consequence,
because the female bee,
has a daddy you see,
but the drone is due to his absence.


Go wonderous creature, mount where science guides
go measure earth, weigh air, state the tides,
instruct the planets in what orbs to run
correct old time, regulate the sun

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Veritas by Kanwarpreet Grewal is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.